A new glance to the Alt-Caffarelli-Friedman monotonicity formula

Abstract

In this paper we revisit the proof of the Alt-Caffarelli-Friedman monotonicity formula. Then, in the framework of the Heisenberg group, we discuss the existence of an analogous monotonicity formula introducing a necessary condition for its existence, recently proved in [18].

Keywords

• monotonicity formulas
• heisenberg group
• free boundary problems
• two-phase problems